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Zero White Noise Limit through Dirichlet forms, with application to diffusions in a random medium
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  • Published: December 1994

Zero White Noise Limit through Dirichlet forms, with application to diffusions in a random medium

  • Pierre Mathieu1 

Probability Theory and Related Fields volume 99, pages 549–580 (1994)Cite this article

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  • 30 Citations

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Summary

We study the Zero White Noise Limit for diffusions in a continuous multidimensional medium: given a continuous function on ℝn,W, we consider diffusions whose drift term is the gradient ofW and whose diffusion coefficient is constant equal to ε. We describe the asymptotics of the exit time from a domain and of the law of the process when ε tends to zero. By applying these results to a random self-similar mediumW we prove limit theorems for a diffusion in a random medium. Our theorems agree with results usually proved through the large deviation principle, although, in our setup, this last tool is not available. We extend to the multidimensional case properties of diffusions in a random medium already known in one dimension.

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Authors and Affiliations

  1. Case J. URA 225, Université de Provence, 3 place Victor Hugo, F-13003, Marseille, France

    Pierre Mathieu

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  1. Pierre Mathieu
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Mathieu, P. Zero White Noise Limit through Dirichlet forms, with application to diffusions in a random medium. Probab. Th. Rel. Fields 99, 549–580 (1994). https://doi.org/10.1007/BF01206232

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  • Received: 30 November 1993

  • Revised: 07 February 1994

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01206232

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Keywords

  • Diffusion Coefficient
  • Continuous Function
  • Stochastic Process
  • White Noise
  • Probability Theory
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